What is the GCF?
This is the GCF between these two numbers.
12 and 18
What is 6?
Factor: x² + 5x
What is x(x + 5)
Factor: x² + 7x + 10.
What is (x + 5)(x + 2)?
Solve: x² - 9 = 0
What is x = 3 and x = -3?
A rectangular garden has an area of x² + 7x + 12 square feet. Its length is x + 3 feet. What is its width?
(x² + 7x + 12) ÷ (x + 3) = x + 4)
This is the GCF between these two numbers.
24 and 36
What is 12?
Factor: 3x² + 9x.
What is 3x(x + 3)?
Factor: x² - 5x + 6
What is (x - 2)(x - 3)?
Solve: x² - 5x = 0.
What is x = 0 and x = 5?
The product of two consecutive integers is 90. Set up and solve a quadratic equation to find the integers.
x(x + 1) = 90 → x² + x - 90 = 0 → (x - 9)(x + 10) = 0 → x = 9 or -10)
This is the GCF between these two terms.
15x² and 25x
What is 5x
Factor: 4x² - 12x.
What is 4x(x - 3)?
Factor: 2x² + 7x + 3
What is (2x + 1)(x + 3)?
Solve: 4x² - 25 = 0
What is x = ±5/2
A square piece of cloth has an area of 4x² - 25 square inches. What are its possible side lengths?
Answer: (2x−5)(2x+5)
Factor our the GCF.
18x³ + 27x²
What is 9x^2(2x+3)?
Factor: -5x² + 15x
What is -5x(x - 3)?
Factor 3x² - 11x - 4.
What is (3x + 1)(x - 4)?
Solve: x² - 3x - 10 = 0
What is x = 5, x = -2
A rocket follows a quadratic path given by -2x² + 18x. Factor the equation and determine when the rocket lands.
(Answer: -2x(x - 9) → x = 0 or x = 9, so it lands at 9 seconds)
Factor our the GCF.
-40x⁴ + 32x³
What is -8x^3(5x-4)?
Factor -6x² - 24x
What is -6x(x + 4)?
Factor: -4x² + 12x - 8.
What is -4(x - 2)(x - 1)?
Solve: -3x² + 12x = 0
What is x = 0, x = 4
The area of a rectangle is given by -3x² + 21x. Factor completely and determine the possible expressions for length and width.
Answer: -3x(x - 7), so possible dimensions are -3x and (x - 7)